Analysis of zz-www.sudokuoftheday.co.uk-20190202-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019

position: .2......6....63.........2.95..3..9.2.8...9.47.7...5.....7.8...1..4........15.286. initial

Autosolve

position: .2..9...6...263..86...5.2.95.63.7982.8.6.9547.7.8.5613257486391864931725..1572864 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 3,8 => CTR => C1: 5
* PRF # C1: 5 => SOL
* PRF # A1: 3,4 => SOL
* PRF # A1: 1,4 => SOL
* DIS # A2: 1,4 => CTR => A2: 7,9
* PRF # A2: 7,9 => SOL
* PRF # B2: 1,4 => SOL
* DIS # B2: 9 => CTR => B2: 1,4
* DIS # H1: 5,7 => CTR => H1: 3
* PRF # H1: 3 => SOL
* PRF # H1: 3,7 => SOL
* DIS # H1: 5 => CTR => H1: 3,7
* PRF # B2: 1,4 => SOL
* DIS # B2: 9 => CTR => B2: 1,4
* DIS # B3: 1,4 => CTR => B3: 3
* PRF # B3: 3 => SOL
* DIS # A1: 1,3 => CTR => A1: 4,7
* DIS # A2: 4,9 => CTR => A2: 1,7
* CNT  18 HDP CHAINS /  22 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # C1: 3,8 => CTR => C1: 5
* PRF C1: 5 => SOL
* STA C1: 5
* CNT   2 HDP CHAINS /   1 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

.2......6....63.........2.95..3..9.2.8...9.47.7...5.....7.8...1..4........15.286. initial
.2..9...6...263..86...5.2.95.63.7982.8.6.9547.7.8.5613257486391864931725..1572864 autosolve
425798136719263458638154279546317982183629547972845613257486391864931725391572864 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
C2: 5,9
C3: 3,8
D1: 1,7
F1: 4,8
D3: 1,7
F3: 4,8
G1: 1,4
G2: 1,4
H2: 5,7
H3: 3,7
B4: 1,4
A5: 1,3
C5: 2,3
A6: 4,9
C6: 2,9
E4: 1,4
E5: 1,2
E6: 2,4
A9: 3,9
B9: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,D3: 1.. / D1 = 1  =>  0 pairs (X) / D3 = 1  =>  0 pairs (_)
G1,G2: 1.. / G1 = 1  =>  0 pairs (*) / G2 = 1  =>  0 pairs (X)
B4,A5: 1.. / B4 = 1  =>  0 pairs (X) / A5 = 1  =>  0 pairs (_)
E4,E5: 1.. / E4 = 1  =>  0 pairs (*) / E5 = 1  =>  0 pairs (X)
B3,D3: 1.. / B3 = 1  =>  0 pairs (X) / D3 = 1  =>  0 pairs (_)
B4,E4: 1.. / B4 = 1  =>  0 pairs (X) / E4 = 1  =>  0 pairs (_)
A5,E5: 1.. / A5 = 1  =>  0 pairs (*) / E5 = 1  =>  0 pairs (X)
C5,C6: 2.. / C5 = 2  =>  0 pairs (X) / C6 = 2  =>  0 pairs (_)
E5,E6: 2.. / E5 = 2  =>  0 pairs (*) / E6 = 2  =>  0 pairs (X)
C5,E5: 2.. / C5 = 2  =>  0 pairs (X) / E5 = 2  =>  0 pairs (_)
C6,E6: 2.. / C6 = 2  =>  0 pairs (*) / E6 = 2  =>  0 pairs (X)
H1,H3: 3.. / H1 = 3  =>  0 pairs (*) / H3 = 3  =>  0 pairs (X)
A5,C5: 3.. / A5 = 3  =>  0 pairs (X) / C5 = 3  =>  0 pairs (_)
A9,B9: 3.. / A9 = 3  =>  0 pairs (*) / B9 = 3  =>  0 pairs (X)
B3,B9: 3.. / B3 = 3  =>  0 pairs (*) / B9 = 3  =>  0 pairs (X)
F1,F3: 4.. / F1 = 4  =>  0 pairs (X) / F3 = 4  => 19 pairs (_)
G1,G2: 4.. / G1 = 4  => 18 pairs (_) / G2 = 4  =>  0 pairs (*)
B4,A6: 4.. / B4 = 4  =>  0 pairs (*) / A6 = 4  =>  0 pairs (X)
E4,E6: 4.. / E4 = 4  =>  0 pairs (X) / E6 = 4  =>  0 pairs (_)
B3,F3: 4.. / B3 = 4  =>  0 pairs (X) / F3 = 4  => 19 pairs (_)
B4,E4: 4.. / B4 = 4  =>  0 pairs (*) / E4 = 4  =>  0 pairs (X)
A6,E6: 4.. / A6 = 4  =>  0 pairs (X) / E6 = 4  =>  0 pairs (_)
C1,C2: 5.. / C1 = 5  =>  0 pairs (*) / C2 = 5  =>  0 pairs (X)
H1,H2: 5.. / H1 = 5  =>  0 pairs (X) / H2 = 5  =>  0 pairs (_)
C1,H1: 5.. / C1 = 5  =>  0 pairs (*) / H1 = 5  =>  0 pairs (X)
C2,H2: 5.. / C2 = 5  =>  0 pairs (X) / H2 = 5  =>  0 pairs (_)
A1,A2: 7.. / A1 = 7  =>  0 pairs (X) / A2 = 7  =>  0 pairs (_)
D1,D3: 7.. / D1 = 7  =>  0 pairs (*) / D3 = 7  =>  0 pairs (X)
A2,H2: 7.. / A2 = 7  =>  0 pairs (*) / H2 = 7  =>  0 pairs (X)
D3,H3: 7.. / D3 = 7  =>  0 pairs (X) / H3 = 7  =>  0 pairs (_)
C1,C3: 8.. / C1 = 8  =>  0 pairs (X) / C3 = 8  => 19 pairs (_)
F1,F3: 8.. / F1 = 8  => 19 pairs (_) / F3 = 8  =>  0 pairs (X)
C1,F1: 8.. / C1 = 8  =>  0 pairs (X) / F1 = 8  => 19 pairs (_)
C3,F3: 8.. / C3 = 8  => 19 pairs (_) / F3 = 8  =>  0 pairs (X)
A6,C6: 9.. / A6 = 9  =>  0 pairs (*) / C6 = 9  =>  0 pairs (X)
A9,B9: 9.. / A9 = 9  =>  0 pairs (X) / B9 = 9  =>  0 pairs (_)
B2,B9: 9.. / B2 = 9  =>  0 pairs (X) / B9 = 9  =>  0 pairs (_)
C2,C6: 9.. / C2 = 9  =>  0 pairs (*) / C6 = 9  =>  0 pairs (X)
* DURATION: 0:00:45.920673  START: 03:24:27.395206  END: 03:25:13.315879 2019-05-01
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A9,B4,B9,C2,C3,C5,C6,D1,D3,E4,E5,E6,F1,F3,G1,G2,H2,H3)
* .2..9...6...263..86...5.2.95.63.7982.8.6.9547.7.8.5613257486391864931725..1572864
* PAIR C3: 3,8 BLK 1
C1: 3,8,5                                # reduction candidate for 3,8
C1: 3,8 => CTR
* 723198456.952631786187542395463.7982.8.6.9547.79825613257486391864931725.31572864
C1: 5 => SOLVED
* 425798136719263458638154279546317982183629547972845613257486391864931725391572864
* PAIR D1: 1,7 ROW 1
A1: 1,7,3,4                              # reduction candidate for 1,7
A1: 3,4 => SOLVED
* 425798136719263458638154279546317982183629547972845613257486391864931725391572864
A1: 1,7                                  # 20 pairs
* PAIR G1: 1,4 ROW 1
A1: 1,4,3,7                              # reduction candidate for 1,4
A1: 1,4 => SOLVED
* 425798136719263458638154279546317982183629547972845613257486391864931725391572864
A1: 3,7                                  # 21 pairs
* PAIR G2: 1,4 ROW 2
A2: 1,4,7,9                              # reduction candidate for 1,4
A2: 1,4 => CTR
* 72.19.4.6...26317861.7542395463179821836295479728.5613257486391864931725..1572864
A2: 7,9 => SOLVED
* 425798136719263458638154279546317982183629547972845613257486391864931725391572864
B2: 1,4,9                                # reduction candidate for 1,4
B2: 1,4 => SOLVED
* 425798136719263458638154279546317982183629547972845613257486391864931725391572864
B2: 9 => CTR
* 723198456495263.786..75.2395.63.7982.8.6.9547.79825613257486391864931725931572864
* PAIR H2: 5,7 BLK 3
H1: 5,7,3                                # reduction candidate for 5,7
H1: 5,7 => CTR
* .2..9...6.95263.786.87542395463179821836.9547.7.8.5613257486391864931725.31572864
H1: 3 => SOLVED
* 425798136719263458638154279546317982183629547972845613257486391864931725391572864
* PAIR H3: 3,7 BLK 3
H1: 3,7,5                                # reduction candidate for 3,7
H1: 3,7 => SOLVED
* 425798136719263458638154279546317982183629547972845613257486391864931725391572864
H1: 5 => CTR
* 723198456.952631786187542395463.7982.8.6.9547.79825613257486391864931725.31572864
* PAIR B4: 1,4 COL B
B2: 1,4,9                                # reduction candidate for 1,4
B2: 1,4 => SOLVED
* 425798136719263458638154279546317982183629547972845613257486391864931725391572864
B2: 9 => CTR
* 723198456495263.786..75.2395.63.7982.8.6.9547.79825613257486391864931725931572864
B3: 1,4,3                                # reduction candidate for 1,4
B3: 1,4 => CTR
* 723198456495263.786..75.2395.63.7982.8.6.9547.79825613257486391864931725931572864
B3: 3 => SOLVED
* 425798136719263458638154279546317982183629547972845613257486391864931725391572864
* PAIR A5: 1,3 COL A
A1: 1,3,4,7                              # reduction candidate for 1,3
A1: 1,3 => CTR
* .2..9...67..263.586...5.2.95.63.7982.8.6.95474798.5613257486391864931725..1572864
A1: 4,7                                  # 21 pairs
* PAIR A6: 4,9 COL A
A2: 4,9,1,7                              # reduction candidate for 4,9
A2: 4,9 => CTR
* 72.19.4.6...26317861.7542395463179821836295479728.5613257486391864931725..1572864
A2: 1,7                                  # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190202-absurd-base-pr-000.dot
* REASONING
* DIS # C1: 3,8 => CTR => C1: 5
* PRF # C1: 5 => SOL
* PRF # A1: 3,4 => SOL
* PRF # A1: 1,4 => SOL
* DIS # A2: 1,4 => CTR => A2: 7,9
* PRF # A2: 7,9 => SOL
* PRF # B2: 1,4 => SOL
* DIS # B2: 9 => CTR => B2: 1,4
* DIS # H1: 5,7 => CTR => H1: 3
* PRF # H1: 3 => SOL
* PRF # H1: 3,7 => SOL
* DIS # H1: 5 => CTR => H1: 3,7
* PRF # B2: 1,4 => SOL
* DIS # B2: 9 => CTR => B2: 1,4
* DIS # B3: 1,4 => CTR => B3: 3
* PRF # B3: 3 => SOL
* DIS # A1: 1,3 => CTR => A1: 4,7
* DIS # A2: 4,9 => CTR => A2: 1,7
* CNT  18 HDP CHAINS /  22 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A9,B4,B9,C2,C3,C5,C6,D1,D3,E4,E5,E6,F1,F3,G1,G2,H2,H3)
* .2..9...6...263..86...5.2.95.63.7982.8.6.9547.7.8.5613257486391864931725..1572864
* PAIR C3: 3,8 BLK 1
C1: 3,8,5                                # reduction candidate for 3,8
C1: 3,8 => CTR
* 723198456.952631786187542395463.7982.8.6.9547.79825613257486391864931725.31572864
C1: 5 => SOLVED
* 425798136719263458638154279546317982183629547972845613257486391864931725391572864
* DURATION: 0:00:02.327791  START: 03:25:31.208675  END: 03:25:33.536466 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190202-absurd-base-pr-001.dot
* REASONING
* DIS # C1: 3,8 => CTR => C1: 5
* PRF C1: 5 => SOL
* STA C1: 5
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190202, absurd

Solution

position: 425798136719263458638154279546317982183629547972845613257486391864931725391572864 solved
Solution

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* DIS # C1: 3,8 => CTR => C1: 5
* PRF # C1: 5 => SOL
* INC # A1: 1,7 => UNS
* PRF # A1: 3,4 => SOL
* PRF # A1: 1,4 => SOL
* INC # A1: 3,7 => UNS
* DIS # A2: 1,4 => CTR => A2: 7,9
* PRF # A2: 7,9 => SOL
* PRF # B2: 1,4 => SOL
* DIS # B2: 9 => CTR => B2: 1,4
* DIS # H1: 5,7 => CTR => H1: 3
* PRF # H1: 3 => SOL
* PRF # H1: 3,7 => SOL
* DIS # H1: 5 => CTR => H1: 3,7
* PRF # B2: 1,4 => SOL
* DIS # B2: 9 => CTR => B2: 1,4
* DIS # B3: 1,4 => CTR => B3: 3
* PRF # B3: 3 => SOL
* DIS # A1: 1,3 => CTR => A1: 4,7
* INC # A1: 4,7 => UNS
* DIS # A2: 4,9 => CTR => A2: 1,7
* INC # A2: 1,7 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C1: 3,8 => CTR => C1: 5
* PRF C1: 5 => SOL
* STA C1: 5
* CNT   2 HDP CHAINS /   1 HYP OPENED